Table 3: Comparison of models trained with different representations of protein structure across various tasks, on a random data split . The optimal choice of representation depends on the task. Shown are mean and standard deviation across four runs with different seeds. Table 4: Comparison of models trained with different representations of protein structure across various tasks, on a sequence data split . Table 5: Comparison of models trained with different representations of protein structure across various tasks, on a structure data split .

This highlights an urgent need of contributions from the machine learning community.

Foundation models have made significant strides in understanding the genomic language of DNA sequences. However, previous models typically adopt the tok-enization methods designed for natural language, which are unsuitable for DNA sequences due to their unique characteristics. In addition, the optimal approach to tokenize DNA remains largely under-explored, and may not be intuitively understood by humans even if discovered. To address these challenges, we introduce MxDNA, a novel framework where the model autonomously learns an effective DNA tokenization strategy through gradient decent.

Z that represents some transfer of mass between elements of w and v . The proof is the same for W . Proposition 2. Suppose that the target row and column representative distributions are the same, The the Kantorovich OT problem and whose rank is at most min(rank(Z), rank( W)) . Proof of proposition 2. From linear algebra, we have that Proof of proposition 3. We suppose that The optimal transport problem can be formulated and solved as the Earth Mover's Distance (EMD) We report the biclustering performance on the synthetic datasets in table 2. At least one of our models finds the perfect partition in all cases. The gene-expression matrices used are the Cumida Breast Cancer and Leukemia datasets. Their characteristics are shown in Table 3. Table 3: Characteristics of the gene expression datasets.

Measuring and making DNA is central to modern biology and biomedicine.

Haplotype assembly and viral quasispecies reconstruction are challenging tasks concerned with analysis of genomic mixtures using sequencing data.